How to Convert the Equation to Polar Form Using Variables r and 8 for x and y?

To convert the Cartesian equation involving x and y into polar form, we use the relationships between Cartesian and polar coordinates:

• x = r * cos(θ)
• y = r * sin(θ)
• r = √(x² + y²)

Let’s assume you have an equation in the form of f(x, y) = k. To convert this equation to polar form, follow these steps:

1. Substitute x and y in terms of r and θ.
2. Replace any constants or coefficients as necessary with their polar equivalents.
3. Simplify the equation to express it solely in terms of r and θ.

For instance, if we start with the equation x² + y² = 64, it can be rewritten in polar form as:

r² = 64

Taking the square root gives:

r = 8

This is the polar form of the original equation, indicating a circle of radius 8 centered at the origin in the polar coordinate system.